Download Refraction of light

Refraction of light
Simone Zuccher
February 4, 2013
Contents
1 The physical phenomenon
1
2 Laws of refraction
2
3 Visible light wavelength dispersion
3
4 Critical angle and total internal reflection
3
5 Conclusion
4
6 Questions
4
1
The physical phenomenon
vious fact. Light is refracted when it leaves water, giving
rise to the illusion that objects in water appear to be both
distorted and closer than they really are.
As early as the first century (A.D.), the ancient Greek
astronomer and geographer Ptolemy attempted to mathematically explain the amount of bending (or refraction)
that occurred, but his proposed law was later determined to
be unreliable. During the 1600s, the Dutch mathematician
Willebrord Snell succeeded in developing a law that defined
a value related to the ratio of the incident and refracted angles, which has subsequently been termed the bending power
or refractive index of a substance. In effect, the more a substance is able to bend or refract light, the larger its refractive
index value is said to be. The pencil in water appears to be
bent because light rays coming from the pencil are abruptly
bent at the air-water interface before reaching our eyes. To
his disappointment, Snell never discovered the reason for
this refraction effect.
In 1678, another Dutch scientist, Christiaan Huygens
devised a mathematical relationship to explain Snell’s observations and proposed that the refractive index of a material is related to the speed at which light travels through
the substance. Huygens determined that the ratio relating
the angles of light paths in two materials having differing
refractive indices should be equal to the ratio of the velocity that light travels when passing through each material.
Thus, he postulated, light would travel more slowly through
materials having a greater refractive index. Stated another
way, the velocity of light through a material is inversely proportional to its refractive index. Although this point has
since been verified experimentally, it was not immediately
obvious to a majority of seventeenth and eighteenth century
investigators who lacked a reliable means to measure the velocity of light. To these scientists, light appeared to travel
at the same speed, regardless of the material through which
it passed. It was over 150 years after Huygens passed away
that the speed of light was measured with enough accuracy
Refraction is a physical phenomenon that occurs every time
a wave, such as light or sound, travels from one medium
(substance) to another in which its speed of propagation is
different. The visible effect is a change in the direction of
the propagating wave from the first to the second medium.
If the incident ray hits the interface (boundary) between
the two media forming a 90◦ angle, then nothing happens
and the ray continues its propagation in the same direction
normal to the interface. If the incident ray does not hit normally the interface between the two media, then a change
in the direction of wave propagation occurs causing strange
effects such as the apparent bending of an object that is
partially submerged in water (see figure 1) or the mirages
observed on a hot, sandy desert.
Figure 1: An everyday experience of refraction
For centuries, man had noticed this rather odd, but ob1
to prove his theories correct.
Expanding on the previous ideas, the absolute refractive
index n of a transparent substance or material is defined as
the relative speed at which light moves through the material
with respect to its speed in a vacuum. Mathematically its
definition is
c
n= ,
v
where c is the speed of light in a vacuum, and v is the velocity of light in the material.
Material
Air
Water
Glycerin
Immersion Oil
Glass (Crown – convex lens)
Glass (Flint – concave lens )
Zircon
Diamond
Lead Sulfide (galena)
Refractive Index
1.0003
1.333
1.473
1.515
1.520
1.656
1.920
2.417
3.910
Figure 2: Definition of normal, incident ray and refracted
ray
The laws of refraction state that
Table 1: List of refractive indices for common materials
1. The incident ray, the normal, and the refracted
ray are coplanar;
Obviously, the absolute index of refraction of a vacuum
2. The ratio of sines of the angles of incidence and
is 1.0, whereas the absolute index of refraction of all other
refraction is equal to the ratio of refractive intransparent materials exceeds the value of 1.0 because light
dices of the second and first medium, i.e.
attains its maximum speed in a vacuum (which is devoid of
sin î
nr
any material). For most practical purposes, the refractive
Snell’s Law,
=
sin r̂
ni
index of air (1.0003) is so close to that of a vacuum that it
can be employed to calculate refractive indices of unknown
where nr is the absolute refractive index of the
materials. The measured refractive indices of several commedium in which the refracted ray travels (second mamon transparent materials are reported in table 1. Materiterial), and ni is the absolute refractive index of the
als with higher refractive indices slow the speed of light to
medium in which the incident ray travels (first matea greater degree than those with lower refractive indices. In
rial).
effect, these materials are said to be more refractive, and
they exhibit a larger angle of refraction for incoming light Snell’s Law describes the relationship between the angles of
rays passing through an air interface
the two light waves and the indices of refraction of the two
materials. When a light wave passes from a less refractive
medium (such as air) to a more refractive medium (such
as water), the velocity of the wave decreases. Conversely,
2 Laws of refraction
when light passes from a more refractive medium (water)
to a less refractive medium (air), the velocity of the wave
With reference to figure 2, we define
increases. The angle of incidence in the first medium, with
• the incident ray as the ray approaching the interface respect to the normal, and the angle of refraction in the second medium (also with respect to the normal), will differ in
between the two media;
proportion to the difference in indices of refraction between
• the point of incidence as the point where the incident the two substances. If a light wave passes from a medium of
lower refractive index to one of higher refractive index, it is
ray strikes the interface;
bent toward the normal. However, if the wave travels from
• the refracted ray as the ray leaving the boundary a medium of higher refractive index to a medium of lower
refractive index, it is bent away from the normal.
through the second medium;
Rearranged to in a different form, Snell’s Law demonstrates
that the ratio of the sines of the incident and re• the normal as the construction line drawn perpendicfracted
angles is equal to a constant which is the ratio of
ular to the boundary at the point of incidence;
the light velocities (or indices of refraction) in the two me• the angle of incidence î as the angle between the in- dia. In fact
c
vi
nr
sin î
cident ray and the normal;
=
= vcr = .
sin r̂
ni
vr
vi
• the angle of refraction r̂ as the angle between the normal and the refracted ray.
The ratio nr /ni is termed the relative index of refraction
for those two substances.
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the prism, an ordered spectrum of color was projected onto
a screen placed behind the prism.
Figure 3: The virtual image seen by the observer seems to
be less deep than what it really is
A number of phenomena that result from light refraction
are often observed in everyday life. A part from the “broken
pencil” of figure 1, one of the most common is experienced
by nearly everyone who has tried to reach for and touch
something submerged in water. An object seen in the water
will usually appear to be at a different depth than it actually is, due to the refraction of light rays as they travel from
the water into the air, as shown in figure 3. The eyes and
brain trace the light rays back into the water as though they
had not refracted, but traveled from the object in a straight
line, creating a virtual image of the object that appears at
a shallower depth.
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Visible light wavelength dispersion
Although reference is usually made to a standard and fixed
refractive index for a substance, careful measurements indicate that the index of refraction for a particular material
varies with the frequency (and wavelength) of radiation, or
the color of visible light. In other words, a substance has
many refractive indices that may differ either marginally, or
to a significant degree, as the color or wavelength of light
is changed. This variation occurs for nearly all transparent
media and has been termed dispersion. The degree of dispersion exhibited by a specific material is dependent upon
how much the refractive index changes with wavelength. For
any substance, as the wavelength of light increases, the refractive index (or the bending of light) decreases. In other
words, blue light, which comprises the shortest wavelength
region in visible light, is refracted at significantly greater
angles than is red light, which has the longest wavelengths.
It is the dispersion of light by ordinary glass that is responsible for the familiar splitting of light into its component
colors by a prism.
In the late seventeenth century, Sir Isaac Newton performed a series of experiments that led to his discovery of the
visible light spectrum, and demonstrated that white light is
composed of an ordered array of colors starting with blue
at one end and progressing through green, yellow, and orange, finally ending with red at the other end. Working in
a darkened room, Newton placed a glass prism in front of
a narrow beam of sunlight emerging through a hole drilled
into a window shutter. When the sunlight passed through
Figure 4: Light dispersion, Newton’s experiment
From this experiment, Newton concluded that white light
is produced from a mixture of many colors, and that the
prism spread or “dispersed” white light by refracting each
color at a different angle so they could be easily separated
(figure 4). Newton was unable to further subdivide the individual colors, which he attempted by passing a single color
of dispersed light through a second prism. However, when
he placed a second prism very close to the first, so that
all of the dispersed colors entered the second prism, Newton found that the colors were recombined to produce white
light again. This finding produced conclusive evidence that
white light is composed of a spectrum of colors that can
easily be separated and reunited.
The phenomenon of dispersion plays a critical role in a
wide variety of common observations. Rainbows result when
sunlight is refracted by raindrops falling through the atmosphere, producing a spectacular display of spectral color
that closely mimics that demonstrated with a prism.
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Critical angle and total internal
reflection
Upon passing through a medium of higher refractive index
into a medium of lower refractive index, the path taken by
light waves is determined by the incident angle with respect
to the boundary between the two media. If the incident
angle increases past a specific value (dependent upon the
refractive index of the two media), it reaches a point at
which the angle is so large that no light is refracted into the
medium of lower refractive index, as illustrated in figure 5.
Figure 5: Critical angle and total internal reflection
The critical angle (or limit angle) is defined as the angle of
incidence that causes a refracted angle equal to 90◦ . In other
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words, as long as the angle of incidence is smaller than the
critical angle, refraction occurs, whereas at the critical angle the refracted ray travels along the interface between the
two media and refraction vanishes. For angles of incidence
greater than the critical angle, light is reflected totally back
into the higher refractive index medium. This phenomenon
is termed total internal reflection. Very common applications based on total internal reflection are diamonds and
optical fibers. The cut of the diamond favors total internal reflection. Most rays entering the top of the diamond
will internally reflect until they reach the top face of the
diamond where they exit. This gives diamonds their bright
sparkle. An optical fiber is a glass “hair” which is so thin
that once light enters one end, it can never strike the inside
walls at less than the critical angle. Therefore, the light
undergoes total internal reflection each time it strikes the
wall and only when it reaches the other end is it allowed to
exit the fiber. Optical fibers are used to carry telephone and
computer communications because of several advantages:
1. They can carry much more information in a much
smaller cable.
2. No interference from electromagnet fields results in
“clear” connections.
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Questions
1. When does refraction occur?
2. What illusion does water create when partially submerged objects are observed?
3. Who tried to explain the phenomenon of refraction?
3. No electrical resistance.
4. What is the refractive index?
4. No hazard of electrocution if cable breaks.
5. What did Christiaan Huygens determine about the
relation between the refractive index and light?
Another everyday example of total internal reflection is the
swimming pool. If the interface between air and water is
rather flat (because there are no people in the water), a
person staying underwater can look outside, owing to refraction, if and only if the incident angle is less than the
critical angle. On the contrary, if the incident angle is larger
than the critical one, the person staying underwater can see
inside the pool thanks total internal reflection simply by
looking at the free surface between air and water.
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and even the human eye, rely in a fundamental way on the
fact that light can be focused, refracted, and reflected. The
refraction of light produces a wide variety of phenomena, including mirages, rainbows, and curious optical illusions such
as making fish appear to be swimming in more shallow water
than they really are. Refraction also causes a thick-walled
beer mug to appear fuller than it really is, and deceives us
into thinking the sun is setting several minutes later than it
really does. Millions of people use the power of refraction
to correct faulty vision with eyeglasses and contact lenses,
which enable them to see the world more clearly. By understanding these properties of light, and how to control
them, we are able to view details that are invisible to the
unaided human eye, regardless of whether they are located
on a microscope slide or in a distant galaxy.
Conclusion
6. Why was Huygens’ theory difficult to prove at first?
7. Where does light reach its maximum speed?
8. What does the expression “to hit normally” mean?
9. What is Snell’s Law about?
10. What conclusion did Newton draw after experimenting with prisms?
11. What works as a prism in a rainbow?
Optical devices ranging from microscopes and telescopes to
cameras, charge-coupled devices (CCDs), video projectors,
12. What is the critical angle?
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